# Extra Credit Project: The Spring Constant of Balls

## Potential, kinetic and spring energy of balls

This project may be done by teams of 1-2 individuals.

Your job in this assignment is to measure carefully the energy which can be stored internally in different types of balls. You must choose at least 5 different types of ball; for example, a tennis ball, a basketball, a soccer ball, a super ball, a beach ball.

First, determine the mass and radius of each ball. Make a guess at its composition, and draw a cross-section of each ball showing its interior.

Second, drop each ball at least 3 times from a standard height which is between 10 and 30 feet. You might use a second-story window, or a tall ladder, or the roof of a garage. Measure carefully the distance between the drop point and the ground (or other surface), and try to drop all balls so that their center of mass starts at the standard height. Draw a diagram which shows the drop point, ground surface, location of dropper and other persons. Measure the height of each ball's first bounce, and describe how you do so.

Calculate the potential energy of each ball at the drop point, and the potential energy of each ball at the peak of its first bounce. What fraction of the initial energy was retained through the first bounce?

Assume that each ball acts like a simple spring, with a spring constant k such that the force required to compress the radius of the ball by a distance x is equal to k*x. You should try to apply a known force (F) to each of your balls (say, by placing an object of known mass on top of them) and measure the resulting decrease in diameter (x). Estimate the spring constant k for each ball. What is the spring potential energy stored in the ball if you squish it down so that its radius is x centimeters smaller than the rest radius?

Assume that the gravitational potential energy recovered in the first bounce is equal to the spring potential energy stored in the ball when it hits the ground after being dropped. Determine as best you can the amount by which each ball compresses as it bounces. Make sure that the units are correct!